There are numerous sites saying aspartame is poison and almost as many debunking this as a hoax. For a discussion by one Dr. Stoll, see http://askwaltstollmd.com/archives/aspar.html
For a comprehensive overview of the controversy including links, see http://www.truthminers.com/truth/aspartame.htm
I personally heard of the controversy two decades ago when my daughter was working at the Library of Congress. She had been asked to fetch information on aspartame for a researcher. Having read it, she will not use aspartame to this day.
On the other hand, I have given it up several times, sometimes for months, and noticed no difference whatsoever in my health. I cannot handle sugar well, so until Splenda came out aspartame was the lesser of various evils. Aspartame contains aspartic acid, an amino acid that is sometimes taken as a supplement. Since taking large amounts of some nutrients can cause an imbalance in others, it seems prudent to limit aspartame although I suspect that it is safe for most of us as long as other sources of amino acids are consumed at the same time. But I am not an expert.
I agree with the sources that say some individuals cannot metabolize aspartame well. There are many substances that I cannot metabolize well including caffeine and sugar, but I have not experienced any problems with artificial sweeteners except for some of the ones ending in "ol" such as maltilol, which gives me gas.
Linja